Diffraction Pattern: Why is Vertical Pattern Observed?

[Anupama]

If you place a thin long wire like object horizontally in the path of a laser passed through a slit in order to obtain a diffraction pattern you will get a vertical diffraction pattern not a horizontal one. Why is it so?

 

[sophiecentaur]

The whole basic of diffraction theory is essentially mathematical so there are no satisfactory non-mathematical 'explanations' for what happens.
The effect of an object blocking a coherent beam is exactly the inverse of that of a hole, the same size as the blocking object - which makes sense, because the total amount of energy must remain the same. For convenience, the pattern calculation usually involves considering sources rather than blocking objects.
We are familiar with the interference from two slits ( the first thing we learn about interference). If not, then this reference is a good start. There are three main steps from those simple interference ideas to the full Diffraction thing.
First, notice that the closer the slits are together (the narrower the object), the wider is the diffraction pattern.
Secondly, to get to the two dimensional pattern of a two dimensional set of point sources, you can consider the patterns along the two axes separately and multiply the effects.
Thirdly, to get from an array of point sources to a continuous distribution (the effect of a hole with coherent light shining through it or an object in the path of a coherent beam) you Integrate over the whole of space rather than just summing the discrete points.
So a long, narrow slot will produce very tight diffraction fringes along the long axis (possibly appearing as a single peak, if the slot is long enough) and wide fringes along the narrow axis. A small circular aperture will produce wide spaced circular fringes and a large circular aperture will produce tight fringes.

 

[Anupama]

Thank you for your reply.

 

[my2cts]

There is translational symmetry along the horizontal direction, so the resulting diff pat must exhibit horizontal tranlational invariance.

 

[goniahedron]

The answer is very simple and easily demonstrable. Alas... Anyway, the reason for the vertical pattern is that the distribution of the spectral colours in a ray of light is longitudinal. But, as I was saying, alas...

 

[blue_leaf77]

Anyway, the reason for the vertical pattern is that the distribution of the spectral colours in a ray of light is longitudinal.

I don't really know what you mean by that, but the presence of the vertical pattern is independent of the spectral content of the illuminating light. In fact, as the used light bandwidth becomes broader and broader, up to some extend the fringe contrast will get reduced due to the decreasing temporal coherence.

 

[sophiecentaur]

vertical pattern is independent of the spectral content of the illuminating light.

The vertical pattern is also dependent on the wavelength as the horizontal pattern although it is less marked. That's because the vertical aperture is very narrow, giving a very broad sin(x)/x pattern.The difference in levels of the different wavelengths, way off axis will be measurable but not noticeable in the region that the horizontal pattern is normally viewed. It's all simple diffraction theory here.

 

[sophiecentaur]

There is translational symmetry along the horizontal direction, so the resulting diff pat must exhibit horizontal tranlational invariance.

Hmmm. Only for an infinitely long diffraction grating.

 

[blue_leaf77]

The vertical pattern is also dependent on the wavelength as the horizontal pattern although it is less marked.

Probably I should rephrase my sentence to " the presence of vertical pattern ... ". Because the particular shape of a diffraction pattern is unique to the diffracting object's shape. The change in wavelength center of the bandwidth will only scale the diffraction pattern, whereas the bandwidth will affect the fringe visibility mostly in the higher orders of the diffraction pattern.

 

[goniahedron]

The real reason for the vertical pattern in question is fundamentally linked to the same reason that is responsible for the vertical VBGYOR spectral distribution observed in subjective prismatic experiments, even though in this case it involves monochromatic light and "simple diffraction" effects. Easily demonstrable (as I said earlier) but nonetheless that is also a too lengthy and too inconvenient subject to embark upon here. A good starting point to that end, however, would be an attempt to explain the diffracting spectral display in the picture below.http://newjaccuse.info/wp-content/uploads/2015/01/Snapshot-16-14-01-2015-12-20-PM.png

 

[metatrons]

Basically 2#, 7#,8#,10# are very good physics explanation to your question. For this matter, I can try to give a simple summarized answer for your question:

The diffraction is highly dependent on wavelength. For a good observable diffraction from an opaque object (or a transparent hole), the size of the object (or hole) must be of a very finite times (a few times to a few hundred times) of the wavelength. More specifically, if you observe from visible light (roughly 400nm-720nm), the good diffraction may occur when the size of the object (or hole) are in the magnitude of microns (a few ums~a few hundreds ums). A very large size will make the diffraction pattern in-distinguishable.

In your case, I can assume the diameter of the cross-section of the wire is very small, therefore diffraction may be observable following this direction; while the length of the wire is too long for any observable diffraction. However, if you make a small opaque square light-blocker (with the similar size as your wire cross-section), I am sure you can observe diffraction in both horizontal and vertical direction.

 

[sophiecentaur]

The diffraction is highly dependent on wavelength.

The diffraction pattern is dependent on wavelength but, of course, any situation in which light (any em waves, in fact) has its amplitude or phase tinkered with in an aperture, will produce a diffraction pattern.
It is true to say that even the effect of a lens on a beam of light is, in fact, a diffraction effect. It so happens that, for a concave lens, the diffraction pattern happens to be a near-perfect image of the object and we can analyse what happens in a simpler way than using integration across the aperture, taking into account the path lengths through the lens material.
When you get down to it, everything involving waves in space is Diffraction.

 

[blue_leaf77]

When you get down to it, everything involving waves in space is Diffraction.

Very true, in fact the fundamental formulae for diffraction such as Kirchoff and Rayleigh-Sommerfeld formulae were originally developed in an attempt to solve the the Helmholtz equation. I think it's safe to say that there is a transparent border between "diffraction" and "propagation", for example a phenomenon of beam focusing is also described by diffraction. In general, diffraction is not so different from an arbitrary beam propagation.

 

[just dani ok]

The diffraction pattern is dependent on wavelength but, of course, any situation in which light (any em waves, in fact) has its amplitude or phase tinkered with in an aperture, will produce a diffraction pattern.
It is true to say that even the effect of a lens on a beam of light is, in fact, a diffraction effect. It so happens that, for a concave lens, the diffraction pattern happens to be a near-perfect image of the object and we can analyse what happens in a simpler way than using integration across the aperture, taking into account the path lengths through the lens material.
When you get down to it, everything involving waves in space is Diffraction.

Is diffraction pattern has the same meaning / mechanism as interference pattern?
AFAIK, diffraction only occurs when wave interacts with matter.

 

[sophiecentaur]

Is diffraction pattern has the same meaning / mechanism as interference pattern?
AFAIK, diffraction only occurs when wave interacts with matter.

I think it's fairly well accepted that the general term is Diffraction. That is what happens when a wave hits an obstruction of some sort (matter) and can be reflected, refracted or just blocked. To calculate the resulting pattern involves integrating the contributions of all infinitesimal parts of the wave front. Interference is vastly simpler and it approximates the 'interaction with matter' to the effect of a number (n) of point sources (holes in a sheet or independent antennae, loudspeakers etc.) The Interference pattern is calculated using a plain summation of n terms. It only works on the assumption the size of the holes is small enough that each hole has an omnidirectional diffraction pattern.
Not surprisingly, we start off being taught about the 'Interference' between two infinitely thin slits.

 

[SDKelly]

If you place a thin long wire like object horizontally in the path of a laser passed through a slit in order to obtain a diffraction pattern you will get a vertical diffraction pattern not a horizontal one. Why is it so?

Diffraction can be a difficult concept to understand. To understand it first, think of it as a water wave bending around an obstacle, like a rock or a boat. This helps see what happens when a wave pattern is obstructed by an opaque obstacle. Since light has a short wavelength, it is more difficult to see the diffraction. Nevertheless, through a small slit, or double slit, one can see a diffracting pattern displayed on a light absorbing surface on the other side. This relationship between the slit size, distance from the light absorber, and slit height can all be simply mathematically expressed, but not so easily understood. For the understanding of how such variables are related I suggest looking to the Khan Academy videos. They give a great description of Youngs equation and what happens to the interference patterns as more and more slits are added in front of a light source.
I hope these additional resources prove helpful.